Node setup for realistic transparent plastic
The problem with this kind of model is that the light needs to bounce around inside the glass many times to reach the edges and create the shiny edges.

A glass shader is what you need, but you also need to crank the number of Glossy bounces way up. See this comparison with the default number of Glossy Bounces (top) vs. the maximum number of Glossy Bounces (bottom):



Note that I also increased the total maximum number of bounces.

In the bottom image there is much more edge glow, however the rendering time has also increased by almost 70%. For larger models this effect will probably be even stronger since the light will bounce inside the glass for a longer time.Be aware that if your model is so large or complicated that the light will need more than 1024 bounces to reach an edge you will not get shiny edges there.

The model I used in my example is just a scaled cube with a simple glass shader and an emission shader on one of the faces.




EDIT 1:
Make sure the color of your glass shader is set to (almost) white. Otherwise every bounce will darken the reflected light and there won't be much left for shiny edges. Unfortunatly the default color of the glass shader is grey and the light will not bounce for long.

EDIT 2:
Here is another small test scene:



I gave the edges a slight roughness and used a texture for the displacement of the surface. You can download the .blend file as reference.